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<!DOCTYPE html>
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<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>HermiteSpline - Cesium Documentation</title>
<!--[if lt IE 9]>
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<![endif]-->
<link href="styles/jsdoc-default.css" rel="stylesheet">
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</head>
<body>
<div id="main">
<h1 class="page-title">
<a href="index.html"><img src="Images/CesiumLogo.png" class="cesiumLogo"></a>
HermiteSpline
<div class="titleCenterer"></div>
</h1>
<section>
<header>
</header>
<article>
<div class="container-overview">
<div class="nameContainer">
<h4 class="name" id="HermiteSpline">
<a href="#HermiteSpline" class="doc-link"></a>
new Cesium.HermiteSpline<span class="signature">(options)</span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L167">Core/HermiteSpline.js 167</a>
</div>
</h4>
</div>
<div class="description">
A Hermite spline is a cubic interpolating spline. Points, incoming tangents, outgoing tangents, and times
must be defined for each control point. The outgoing tangents are defined for points [0, n - 2] and the incoming
tangents are defined for points [1, n - 1]. For example, when interpolating a segment of the curve between <code>points[i]</code> and
<code>points[i + 1]</code>, the tangents at the points will be <code>outTangents[i]</code> and <code>inTangents[i]</code>,
respectively.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>options</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last">
Object with the following properties:
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>times</code></td>
<td class="type">
<span class="param-type">Array.&lt;Number></span>
</td>
<td class="description last">
An array of strictly increasing, unit-less, floating-point times at each point.
The values are in no way connected to the clock time. They are the parameterization for the curve.</td>
</tr>
<tr>
<td class="name"><code>points</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of <a href="Cartesian3.html"><code>Cartesian3</code></a> control points.</td>
</tr>
<tr>
<td class="name"><code>inTangents</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of <a href="Cartesian3.html"><code>Cartesian3</code></a> incoming tangents at each control point.</td>
</tr>
<tr>
<td class="name"><code>outTangents</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of <a href="Cartesian3.html"><code>Cartesian3</code></a> outgoing tangents at each control point.</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points.length must be greater than or equal to 2.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: times.length must be equal to points.length.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: inTangents and outTangents must have a length equal to points.length - 1.
</div>
</li>
</ul>
<dl class="details">
<h5>Example:</h5>
<pre><code class="language-javascript">// Create a G&lt;sup>1&lt;/sup> continuous Hermite spline
const times = [ 0.0, 1.5, 3.0, 4.5, 6.0 ];
const spline = new Cesium.HermiteSpline({
times : times,
points : [
new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
],
outTangents : [
new Cesium.Cartesian3(1125196, -161816, 270551),
new Cesium.Cartesian3(-996690.5, -365906.5, 184028.5),
new Cesium.Cartesian3(-2096917, 48379.5, -292683.5),
new Cesium.Cartesian3(-890902.5, 408999.5, -447115)
],
inTangents : [
new Cesium.Cartesian3(-1993381, -731813, 368057),
new Cesium.Cartesian3(-4193834, 96759, -585367),
new Cesium.Cartesian3(-1781805, 817999, -894230),
new Cesium.Cartesian3(1165345, 112641, 47281)
]
});
const p0 = spline.evaluate(times[0]);</code></pre>
<h5>See:</h5>
<ul class="see-list">
<li><a href="CatmullRomSpline.html">CatmullRomSpline</a></li>
<li><a href="LinearSpline.html">LinearSpline</a></li>
<li><a href="QuaternionSpline.html">QuaternionSpline</a></li>
<li><a href="WeightSpline.html">WeightSpline</a></li>
</ul>
</dl>
</div>
<h3 class="subsection-title">Members</h3>
<div class="nameContainer">
<h4 class="name" id="inTangents">
<a href="#inTangents" class="doc-link"></a>
<span class="type-signature attribute-readonly">readonly</span> inTangents<span class="type-signature"> : Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L249">Core/HermiteSpline.js 249</a>
</div>
</h4>
</div>
<div class="description">
An array of <a href="Cartesian3.html"><code>Cartesian3</code></a> incoming tangents at each control point.
</div>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="outTangents">
<a href="#outTangents" class="doc-link"></a>
<span class="type-signature attribute-readonly">readonly</span> outTangents<span class="type-signature"> : Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L263">Core/HermiteSpline.js 263</a>
</div>
</h4>
</div>
<div class="description">
An array of <a href="Cartesian3.html"><code>Cartesian3</code></a> outgoing tangents at each control point.
</div>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="points">
<a href="#points" class="doc-link"></a>
<span class="type-signature attribute-readonly">readonly</span> points<span class="type-signature"> : Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L235">Core/HermiteSpline.js 235</a>
</div>
</h4>
</div>
<div class="description">
An array of <a href="Cartesian3.html"><code>Cartesian3</code></a> control points.
</div>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="times">
<a href="#times" class="doc-link"></a>
<span class="type-signature attribute-readonly">readonly</span> times<span class="type-signature"> : Array.&lt;Number></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L221">Core/HermiteSpline.js 221</a>
</div>
</h4>
</div>
<div class="description">
An array of times for the control points.
</div>
<dl class="details">
</dl>
<h3 class="subsection-title">Methods</h3>
<div class="nameContainer">
<h4 class="name" id=".createC1">
<a href="#.createC1" class="doc-link"></a>
<span class="type-signature attribute-static">static</span> Cesium.HermiteSpline.createC1<span class="signature">(options)</span> &rarr; <span class="type-signature returnType"><a href="HermiteSpline.html">HermiteSpline</a></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L308">Core/HermiteSpline.js 308</a>
</div>
</h4>
</div>
<div class="description">
Creates a spline where the tangents at each control point are the same.
The curves are guaranteed to be at least in the class C<sup>1</sup>.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>options</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last">
Object with the following properties:
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>times</code></td>
<td class="type">
<span class="param-type">Array.&lt;Number></span>
</td>
<td class="description last">
The array of control point times.</td>
</tr>
<tr>
<td class="name"><code>points</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of control points.</td>
</tr>
<tr>
<td class="name"><code>tangents</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of tangents at the control points.</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
A hermite spline.
</div>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points, times and tangents are required.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points.length must be greater than or equal to 2.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: times, points and tangents must have the same length.
</div>
</li>
</ul>
<dl class="details">
<h5>Example:</h5>
<pre><code class="language-javascript">const points = [
new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
];
// Add tangents
const tangents = new Array(points.length);
tangents[0] = new Cesium.Cartesian3(1125196, -161816, 270551);
const temp = new Cesium.Cartesian3();
for (let i = 1; i &lt; tangents.length - 1; ++i) {
tangents[i] = Cesium.Cartesian3.multiplyByScalar(Cesium.Cartesian3.subtract(points[i + 1], points[i - 1], temp), 0.5, new Cesium.Cartesian3());
}
tangents[tangents.length - 1] = new Cesium.Cartesian3(1165345, 112641, 47281);
const spline = Cesium.HermiteSpline.createC1({
times : times,
points : points,
tangents : tangents
});</code></pre>
</dl>
<div class="nameContainer">
<h4 class="name" id=".createClampedCubic">
<a href="#.createClampedCubic" class="doc-link"></a>
<span class="type-signature attribute-static">static</span> Cesium.HermiteSpline.createClampedCubic<span class="signature">(options)</span> &rarr; <span class="type-signature returnType"><a href="HermiteSpline.html">HermiteSpline</a>|<a href="LinearSpline.html">LinearSpline</a></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L437">Core/HermiteSpline.js 437</a>
</div>
</h4>
</div>
<div class="description">
Creates a clamped cubic spline. The tangents at the interior control points are generated
to create a curve in the class C<sup>2</sup>.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>options</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last">
Object with the following properties:
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>times</code></td>
<td class="type">
<span class="param-type">Array.&lt;Number></span>
</td>
<td class="description last">
The array of control point times.</td>
</tr>
<tr>
<td class="name"><code>points</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of control points.</td>
</tr>
<tr>
<td class="name"><code>firstTangent</code></td>
<td class="type">
<span class="param-type"><a href="Cartesian3.html">Cartesian3</a></span>
</td>
<td class="description last">
The outgoing tangent of the first control point.</td>
</tr>
<tr>
<td class="name"><code>lastTangent</code></td>
<td class="type">
<span class="param-type"><a href="Cartesian3.html">Cartesian3</a></span>
</td>
<td class="description last">
The incoming tangent of the last control point.</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
A hermite spline or a linear spline if less than 3 control points were given.
</div>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points, times, firstTangent and lastTangent are required.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points.length must be greater than or equal to 2.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: times.length must be equal to points.length.
</div>
</li>
</ul>
<dl class="details">
<h5>Example:</h5>
<pre><code class="language-javascript">// Create a clamped cubic spline above the earth from Philadelphia to Los Angeles.
const spline = Cesium.HermiteSpline.createClampedCubic({
times : [ 0.0, 1.5, 3.0, 4.5, 6.0 ],
points : [
new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
],
firstTangent : new Cesium.Cartesian3(1125196, -161816, 270551),
lastTangent : new Cesium.Cartesian3(1165345, 112641, 47281)
});</code></pre>
</dl>
<div class="nameContainer">
<h4 class="name" id=".createNaturalCubic">
<a href="#.createNaturalCubic" class="doc-link"></a>
<span class="type-signature attribute-static">static</span> Cesium.HermiteSpline.createNaturalCubic<span class="signature">(options)</span> &rarr; <span class="type-signature returnType"><a href="HermiteSpline.html">HermiteSpline</a>|<a href="LinearSpline.html">LinearSpline</a></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L368">Core/HermiteSpline.js 368</a>
</div>
</h4>
</div>
<div class="description">
Creates a natural cubic spline. The tangents at the control points are generated
to create a curve in the class C<sup>2</sup>.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>options</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last">
Object with the following properties:
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>times</code></td>
<td class="type">
<span class="param-type">Array.&lt;Number></span>
</td>
<td class="description last">
The array of control point times.</td>
</tr>
<tr>
<td class="name"><code>points</code></td>
<td class="type">
<span class="param-type">Array.&lt;<a href="Cartesian3.html">Cartesian3</a>></span>
</td>
<td class="description last">
The array of control points.</td>
</tr>
</tbody>
</table>
</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
A hermite spline or a linear spline if less than 3 control points were given.
</div>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points and times are required.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: points.length must be greater than or equal to 2.
</div>
</li>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: times.length must be equal to points.length.
</div>
</li>
</ul>
<dl class="details">
<h5>Example:</h5>
<pre><code class="language-javascript">// Create a natural cubic spline above the earth from Philadelphia to Los Angeles.
const spline = Cesium.HermiteSpline.createNaturalCubic({
times : [ 0.0, 1.5, 3.0, 4.5, 6.0 ],
points : [
new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
]
});</code></pre>
</dl>
<div class="nameContainer">
<h4 class="name" id="clampTime">
<a href="#clampTime" class="doc-link"></a>
clampTime<span class="signature">(time)</span> &rarr; <span class="type-signature returnType">Number</span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L537">Core/HermiteSpline.js 537</a>
</div>
</h4>
</div>
<div class="description">
Clamps the given time to the period covered by the spline.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>time</code></td>
<td class="type">
<span class="param-type">Number</span>
</td>
<td class="description last">
The time.</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
The time, clamped to the animation period.
</div>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="evaluate">
<a href="#evaluate" class="doc-link"></a>
evaluate<span class="signature">(time, <span class="optional">result</span>)</span> &rarr; <span class="type-signature returnType"><a href="Cartesian3.html">Cartesian3</a></span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L550">Core/HermiteSpline.js 550</a>
</div>
</h4>
</div>
<div class="description">
Evaluates the curve at a given time.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>time</code></td>
<td class="type">
<span class="param-type">Number</span>
</td>
<td class="description last">
The time at which to evaluate the curve.</td>
</tr>
<tr>
<td class="name"><code>result</code></td>
<td class="type">
<span class="param-type"><a href="Cartesian3.html">Cartesian3</a></span>
</td>
<td class="description last">
<span class="optional">optional</span>
The object onto which to store the result.</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
The modified result parameter or a new instance of the point on the curve at the given time.
</div>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: time must be in the range <code>[t<sub>0</sub>, t<sub>n</sub>]</code>, where <code>t<sub>0</sub></code>
is the first element in the array <code>times</code> and <code>t<sub>n</sub></code> is the last element
in the array <code>times</code>.
</div>
</li>
</ul>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="findTimeInterval">
<a href="#findTimeInterval" class="doc-link"></a>
findTimeInterval<span class="signature">(time)</span> &rarr; <span class="type-signature returnType">Number</span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L516">Core/HermiteSpline.js 516</a>
</div>
</h4>
</div>
<div class="description">
Finds an index <code>i</code> in <code>times</code> such that the parameter
<code>time</code> is in the interval <code>[times[i], times[i + 1]]</code>.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>time</code></td>
<td class="type">
<span class="param-type">Number</span>
</td>
<td class="description last">
The time.</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
The index for the element at the start of the interval.
</div>
<h5>Throws:</h5>
<ul>
<li>
<div class="param-desc">
<span class="param-type"><a href="DeveloperError.html">DeveloperError</a></span>
: time must be in the range <code>[t<sub>0</sub>, t<sub>n</sub>]</code>, where <code>t<sub>0</sub></code>
is the first element in the array <code>times</code> and <code>t<sub>n</sub></code> is the last element
in the array <code>times</code>.
</div>
</li>
</ul>
<dl class="details">
</dl>
<div class="nameContainer">
<h4 class="name" id="wrapTime">
<a href="#wrapTime" class="doc-link"></a>
wrapTime<span class="signature">(time)</span> &rarr; <span class="type-signature returnType">Number</span>
<div class="source-link rightLinks">
<a href="https://github.com/CesiumGS/cesium/blob/1.91/Source/Core/HermiteSpline.js#L528">Core/HermiteSpline.js 528</a>
</div>
</h4>
</div>
<div class="description">
Wraps the given time to the period covered by the spline.
</div>
<table class="params">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>time</code></td>
<td class="type">
<span class="param-type">Number</span>
</td>
<td class="description last">
The time.</td>
</tr>
</tbody>
</table>
<h5>Returns:</h5>
<div class="param-desc">
The time, wrapped around to the updated animation.
</div>
<dl class="details">
</dl>
</article>
</section>
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